When I was in 8th grade, close to Memorial Day 2000 there was a very strong derecho that moved directly through the MSP area. There was a tornado confirmed over Shoreview (N side if MSP) that was probably F0/F1 max (shingles being ripped off, downed power lines, small trees was the extent.) I don't remember exactly but I dont think any counties were Tornado warned. I know the sirens were sounded in every part of the MSP area. Indeed it was a very nice derecho, knocked out power to much of the MSP area (wind gusts approaching 90mph). This would be a great case, IMO when SVR warnings from NWS would warrant tornado siren usage because the house behind me had a huge tree fall on it. Luckily, the roof held up and they were fine and probably would have been fine if the roof collapsed because they were in the basement thanks to the sirens.
However, I remember a very extreme case when I was in 5th or 6th grade. It was late October, temps in the low 50s... with a very thick strato-cumulus deck. Me and my brother were playing catch when suddenly the tornado sirens went off. Even in 5th grade I knew enough to question it. I came inside, turned on the news and guess what the sirens were sounded for? One random civilian on the north side of town thought they saw a tornado. I dont know what day it was, or even what year... so I can't say I know the weather for that day at all besides what I saw with my eyes. However, I'm sure there were no watches because our neighbor at the time was TERRIFIED of storms and even a flash flood watch (there is no way, even if it rained 3ft that our neighberhood would flood given elevation) would alarm her and she'd be calling every half hour making sure my mom was there in case she had to come over.
My opinion is, sirens should be sounded when there is an imminent threat warned by credible sources. This includes air raids (seems way ancient, I know), and weather, and anything else... for instance in Washington they would sound the sirens if a tsunami was imminent. I really think there need to be national guidelines to follow, but I think it should be up to the local authorities (and meteorologists, or other experts in whatever field of study concerns the danger) to decide on siren/no siren based on the guidelines. The worst case scenario is this: sirens get used so often that the general public begins to ignore them. We all know what can happen from there on out.